You are correct. Double-bracing refers to the legs being double braced. They've made a mistake in their listing of the product.

Double bracing for a throne is good but in a reality, you need a spindle that controls the height of the throne. Because of the added weight of this mechanism, most all thrones will be double-braced anyway. But I would totally avoid thrones that did not have a spindle controlling the height adjustment because you need to lock it from spinning.